Does the use of stents reduce the risk of stroke?
Researchers randomly assigned 224 patients to the treatment group and 227 to the control group.
| group | 30 days_stroke | 30 days_no event | 365 days_stroke | 365 days_no event |
|---|---|---|---|---|
| Control | 13 | 214 | 28 | 199 |
| Treatment | 33 | 191 | 45 | 179 |
Of the 224 patients in the treatment group, 45 had a stroke by the end of the first year. Using these two numbers, compute the proportion of patients in the treatment group who had a stroke by the end of their first year.
Compute the proportion of patients in the control group who had a stroke by the end of the first year.
What do these two summary statistics tell us about the research question “Does the use of stents reduce the risk of stroke?”
Steps in a statistical investigation:
Statistics is the study of how best to collect, analyze, and draw conclusions from data.
| loan_amount | interest_rate | term | grade | state | total_income | homeownership |
|---|---|---|---|---|---|---|
| 22000 | 10.90 | 60 | B | NJ | 59000 | rent |
| 6000 | 9.92 | 36 | B | CA | 60000 | rent |
| 25000 | 26.30 | 36 | E | SC | 75000 | mortgage |
| 6000 | 9.92 | 36 | B | CA | 75000 | rent |
| 25000 | 9.43 | 60 | B | OH | 254000 | mortgage |
| 6400 | 9.92 | 36 | B | IN | 67000 | mortgage |
county Data Frame| name | state | pop2000 | pop2010 | pop2017 | pop_change | poverty | homeownership | multi_unit | unemployment_rate | metro | median_edu | per_capita_income | median_hh_income | smoking_ban |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Autauga County | Alabama | 43671 | 54571 | 55504 | 1.48 | 13.7 | 77.5 | 7.2 | 3.86 | yes | some_college | 27841.70 | 55317 | none |
| Baldwin County | Alabama | 140415 | 182265 | 212628 | 9.19 | 11.8 | 76.7 | 22.6 | 3.99 | yes | some_college | 27779.85 | 52562 | none |
| Barbour County | Alabama | 29038 | 27457 | 25270 | -6.22 | 27.2 | 68.0 | 11.1 | 5.90 | no | hs_diploma | 17891.73 | 33368 | partial |
| Bibb County | Alabama | 20826 | 22915 | 22668 | 0.73 | 15.2 | 82.9 | 6.6 | 4.39 | yes | hs_diploma | 20572.05 | 43404 | none |
| Blount County | Alabama | 51024 | 57322 | 58013 | 0.68 | 15.6 | 82.0 | 3.7 | 4.02 | yes | hs_diploma | 21367.39 | 47412 | none |
| Bullock County | Alabama | 11714 | 10914 | 10309 | -2.28 | 28.5 | 76.9 | 9.9 | 4.93 | no | hs_diploma | 15444.16 | 29655 | none |
| Butler County | Alabama | 21399 | 20947 | 19825 | -2.69 | 24.4 | 69.0 | 13.7 | 5.49 | no | hs_diploma | 17014.95 | 36326 | NA |
| Calhoun County | Alabama | 112249 | 118572 | 114728 | -1.51 | 18.6 | 70.7 | 14.3 | 4.93 | yes | some_college | 23609.64 | 43686 | NA |
| Chambers County | Alabama | 36583 | 34215 | 33713 | -1.20 | 18.8 | 71.4 | 8.7 | 4.08 | no | hs_diploma | 21079.51 | 37342 | none |
| Cherokee County | Alabama | 23988 | 25989 | 25857 | -0.60 | 16.1 | 77.5 | 4.3 | 4.05 | no | hs_diploma | 23067.93 | 40041 | none |
| Chilton County | Alabama | 39593 | 43643 | 44067 | 0.97 | 19.4 | 75.1 | 4.4 | 4.05 | yes | hs_diploma | 22793.82 | 43501 | none |
| Choctaw County | Alabama | 15922 | 13859 | 12945 | -3.37 | 22.3 | 85.6 | 3.9 | 6.39 | no | hs_diploma | 20363.87 | 32122 | none |
| Clarke County | Alabama | 27867 | 25833 | 24083 | -4.12 | 25.3 | 80.0 | 6.3 | 8.48 | no | hs_diploma | 20099.21 | 33827 | none |
| Clay County | Alabama | 14254 | 13932 | 13367 | -0.29 | 19.1 | 72.8 | 11.2 | 4.37 | no | hs_diploma | 20879.67 | 37287 | none |
| Cleburne County | Alabama | 14123 | 14972 | 14900 | -0.51 | 19.1 | 74.9 | 5.3 | 4.46 | no | hs_diploma | 20158.98 | 37396 | none |
| Coffee County | Alabama | 43615 | 49948 | 51874 | 2.42 | 16.1 | 69.7 | 13.6 | 4.39 | no | some_college | 25627.63 | 49821 | none |
| Colbert County | Alabama | 54984 | 54428 | 54500 | -0.05 | 16.8 | 73.5 | 12.3 | 5.21 | yes | some_college | 22915.45 | 45477 | none |
| Conecuh County | Alabama | 14089 | 13228 | 12469 | -3.40 | 26.4 | 81.6 | 6.0 | 6.14 | no | hs_diploma | 14814.23 | 30434 | none |
| Coosa County | Alabama | 12202 | 11539 | 10754 | -4.43 | 14.4 | 83.7 | 1.9 | 4.62 | no | hs_diploma | 19147.01 | 34792 | none |
| Covington County | Alabama | 37631 | 37765 | 37092 | -1.90 | 17.6 | 74.0 | 6.1 | 5.24 | no | hs_diploma | 22146.06 | 39467 | none |
| Crenshaw County | Alabama | 13665 | 13906 | 13871 | 0.17 | 17.6 | 67.8 | 9.2 | 4.47 | no | hs_diploma | 20466.80 | 38937 | none |
| Cullman County | Alabama | 77483 | 80406 | 82755 | 2.58 | 16.4 | 74.7 | 8.5 | 3.71 | no | hs_diploma | 21287.64 | 40997 | none |
| Dale County | Alabama | 49129 | 50251 | 49226 | -1.07 | 19.6 | 61.2 | 13.2 | 4.43 | no | some_college | 22299.61 | 44711 | none |
| Dallas County | Alabama | 46365 | 43820 | 39215 | -6.59 | 31.9 | 62.6 | 16.0 | 7.53 | no | hs_diploma | 18042.21 | 30065 | none |
| DeKalb County | Alabama | 64452 | 71109 | 71617 | 1.00 | 21.5 | 77.5 | 6.4 | 4.49 | no | hs_diploma | 19007.97 | 38842 | none |
| Elmore County | Alabama | 65874 | 79303 | 81677 | 1.39 | 13.5 | 77.6 | 7.0 | 3.64 | yes | some_college | 27266.03 | 54981 | partial |
| Escambia County | Alabama | 38440 | 38319 | 37447 | -0.86 | 23.8 | 73.5 | 7.8 | 5.03 | no | hs_diploma | 18527.38 | 35026 | none |
| Etowah County | Alabama | 103459 | 104430 | 102755 | -1.07 | 17.9 | 73.0 | 11.9 | 4.57 | yes | some_college | 21208.43 | 42064 | none |
| Fayette County | Alabama | 18495 | 17241 | 16468 | -2.11 | 18.1 | 76.0 | 7.9 | 4.73 | no | hs_diploma | 21654.89 | 36541 | none |
| Franklin County | Alabama | 31223 | 31704 | 31495 | -0.03 | 23.0 | 69.2 | 10.4 | 4.23 | no | hs_diploma | 18783.03 | 39501 | partial |
| Geneva County | Alabama | 25764 | 26790 | 26421 | -0.99 | 22.5 | 71.6 | 6.6 | 4.27 | yes | hs_diploma | 20741.87 | 39293 | none |
| Greene County | Alabama | 9974 | 9045 | 8330 | -4.82 | 38.8 | 71.1 | 11.1 | 7.66 | no | hs_diploma | 12330.36 | 20954 | NA |
| Hale County | Alabama | 17185 | 15760 | 14812 | -2.86 | 26.1 | 74.3 | 6.1 | 5.89 | yes | hs_diploma | 19196.55 | 34679 | none |
| Henry County | Alabama | 16310 | 17302 | 17147 | 0.10 | 13.7 | 81.9 | 3.2 | 4.87 | yes | hs_diploma | 23562.00 | 45569 | none |
| Houston County | Alabama | 88787 | 101547 | 104346 | 0.70 | 18.5 | 67.4 | 15.2 | 4.34 | yes | some_college | 23573.18 | 42803 | none |
| Jackson County | Alabama | 53926 | 53227 | 51909 | -1.92 | 19.0 | 76.6 | 5.8 | 4.77 | no | hs_diploma | 20061.42 | 39281 | NA |
| Jefferson County | Alabama | 662047 | 658466 | 659197 | 0.07 | 17.6 | 66.8 | 24.0 | 4.24 | yes | some_college | 29259.76 | 49321 | none |
| Lamar County | Alabama | 15904 | 14564 | 13946 | -1.86 | 23.1 | 75.1 | 9.0 | 4.23 | no | hs_diploma | 21848.70 | 36016 | none |
| Lauderdale County | Alabama | 87966 | 92709 | 92538 | -0.16 | 16.3 | 73.0 | 14.7 | 4.61 | yes | some_college | 25827.78 | 44888 | none |
| Lawrence County | Alabama | 34803 | 34339 | 33049 | -1.57 | 16.6 | 78.7 | 5.1 | 4.88 | yes | hs_diploma | 21896.84 | 43779 | none |
| Lee County | Alabama | 115092 | 140247 | 161604 | 6.71 | 22.0 | 64.2 | 23.3 | 3.91 | yes | some_college | 26160.00 | 47564 | none |
| Limestone County | Alabama | 65676 | 82782 | 94402 | 6.19 | 14.8 | 77.1 | 9.4 | 3.98 | yes | some_college | 25685.40 | 52831 | none |
| Lowndes County | Alabama | 13473 | 11299 | 10076 | -5.46 | 30.2 | 75.4 | 7.0 | 8.00 | yes | hs_diploma | 18901.26 | 29785 | none |
| Macon County | Alabama | 24105 | 21452 | 18755 | -6.32 | 25.9 | 68.0 | 15.5 | 5.78 | no | hs_diploma | 21921.66 | 32308 | none |
| Madison County | Alabama | 276700 | 334811 | 361046 | 4.24 | 13.6 | 70.4 | 21.4 | 3.85 | yes | some_college | 34416.12 | 61318 | NA |
| Marengo County | Alabama | 22539 | 21027 | 19375 | -3.63 | 25.6 | 73.5 | 8.3 | 5.65 | no | hs_diploma | 20738.37 | 32255 | none |
| Marion County | Alabama | 31214 | 30776 | 29833 | -1.28 | 17.6 | 75.8 | 10.9 | 4.79 | no | hs_diploma | 21682.70 | 35719 | none |
| Marshall County | Alabama | 82231 | 93019 | 95548 | 1.33 | 21.0 | 72.5 | 9.3 | 3.80 | no | hs_diploma | 21785.98 | 41104 | partial |
| Mobile County | Alabama | 399843 | 412992 | 413955 | 0.01 | 19.3 | 68.4 | 17.7 | 5.18 | yes | some_college | 23639.54 | 45802 | none |
| Monroe County | Alabama | 24324 | 23068 | 21327 | -3.83 | 33.7 | 73.8 | 6.0 | 6.74 | no | hs_diploma | 15964.50 | 26036 | none |
| Montgomery County | Alabama | 223510 | 229363 | 226646 | -0.56 | 20.8 | 63.2 | 22.4 | 4.30 | yes | some_college | 26622.04 | 46545 | none |
| Morgan County | Alabama | 111064 | 119490 | 118818 | -0.60 | 16.6 | 73.1 | 13.7 | 4.11 | yes | some_college | 24454.90 | 47529 | partial |
| Perry County | Alabama | 11861 | 10591 | 9339 | -6.79 | 41.9 | 67.8 | 11.4 | 7.94 | no | hs_diploma | 11800.68 | 22973 | none |
| Pickens County | Alabama | 20949 | 19746 | 20176 | 4.53 | 22.9 | 74.1 | 10.1 | 5.29 | yes | hs_diploma | 19887.90 | 36220 | none |
| Pike County | Alabama | 29605 | 32899 | 33267 | -0.88 | 26.3 | 56.3 | 18.7 | 4.88 | no | hs_diploma | 20558.82 | 35684 | none |
| Randolph County | Alabama | 22380 | 22913 | 22670 | 0.55 | 18.7 | 75.9 | 4.8 | 4.40 | no | hs_diploma | 20401.61 | 39485 | none |
| Russell County | Alabama | 49756 | 52947 | 57045 | -3.51 | 20.9 | 62.3 | 17.8 | 4.30 | yes | some_college | 20603.92 | 38988 | none |
| St. Clair County | Alabama | 64742 | 83593 | 88199 | 2.52 | 13.7 | 82.2 | 5.5 | 3.97 | yes | hs_diploma | 24731.80 | 53483 | none |
| Shelby County | Alabama | 143293 | 195085 | 213605 | 4.76 | 8.3 | 80.6 | 11.4 | 3.23 | yes | some_college | 34709.33 | 74063 | NA |
| Sumter County | Alabama | 14798 | 13763 | 12687 | -5.15 | 36.0 | 68.3 | 14.5 | 6.54 | no | hs_diploma | 14308.71 | 21663 | partial |
| Talladega County | Alabama | 80321 | 82291 | 80065 | -1.76 | 19.3 | 73.0 | 9.6 | 4.96 | no | hs_diploma | 21548.16 | 39219 | none |
| Tallapoosa County | Alabama | 41475 | 41616 | 40681 | -0.83 | 21.2 | 73.3 | 8.9 | 4.16 | no | hs_diploma | 22228.57 | 42181 | none |
| Tuscaloosa County | Alabama | 164875 | 194656 | 207811 | 3.52 | 17.3 | 63.3 | 25.4 | 4.14 | yes | some_college | 24579.41 | 50513 | none |
| Walker County | Alabama | 70713 | 67023 | 64058 | -2.57 | 21.5 | 77.7 | 6.6 | 5.02 | yes | hs_diploma | 20704.31 | 38872 | none |
| Washington County | Alabama | 18097 | 17581 | 16531 | -2.11 | 22.0 | 83.0 | 2.6 | 6.84 | no | hs_diploma | 19907.22 | 42185 | none |
| Wilcox County | Alabama | 13183 | 11670 | 10719 | -3.87 | 31.9 | 76.8 | 6.0 | 11.40 | no | hs_diploma | 14415.88 | 27012 | none |
| Winston County | Alabama | 24843 | 24484 | 23722 | -1.91 | 18.7 | 73.8 | 6.1 | 5.00 | no | hs_diploma | 19518.80 | 35362 | none |
| Aleutians East Borough | Alaska | 2697 | 3141 | 3370 | 1.38 | 16.7 | 59.2 | 11.8 | 2.52 | no | hs_diploma | 30891.70 | 66607 | NA |
| Aleutians West Census Area | Alaska | 5465 | 5561 | 5763 | 0.19 | 7.5 | 36.3 | 30.9 | 3.63 | no | hs_diploma | 28443.14 | 85192 | none |
| Anchorage Municipality | Alaska | 260283 | 291826 | 294356 | -2.23 | 8.1 | 61.7 | 35.3 | 5.97 | yes | some_college | 38324.82 | 82271 | none |
| Bethel Census Area | Alaska | 16006 | 17013 | 18076 | 1.28 | 27.0 | 61.3 | 13.9 | 13.79 | no | hs_diploma | 17802.36 | 53853 | none |
| Bristol Bay Borough | Alaska | 1258 | 997 | 867 | -8.93 | 7.1 | 56.6 | 13.4 | 6.34 | no | some_college | 38984.10 | 79500 | none |
| Denali Borough | Alaska | 1893 | 1826 | 2074 | 7.35 | 15.5 | 60.7 | 14.1 | 9.38 | no | some_college | 39316.88 | 83295 | none |
| Dillingham Census Area | Alaska | 4922 | 4847 | 4932 | -0.98 | 16.6 | 60.7 | 14.1 | 9.29 | no | hs_diploma | 21804.82 | 58708 | none |
| Fairbanks North Star Borough | Alaska | 82840 | 97581 | 99703 | -1.18 | 7.7 | 59.8 | 26.2 | 6.29 | yes | some_college | 34968.82 | 76250 | none |
| Haines Borough | Alaska | 2392 | 2508 | 2526 | -1.29 | 8.4 | 74.5 | 13.2 | 9.09 | no | some_college | 37141.41 | 70640 | none |
| Hoonah Angoon Census Area | Alaska | 3436 | 2150 | NA | NA | 11.1 | 64.0 | 8.6 | 12.63 | no | some_college | 29040.32 | 57900 | NA |
| Juneau City and Borough | Alaska | 30711 | 31275 | 32094 | -1.46 | 7.4 | 64.0 | 32.2 | 4.75 | no | some_college | 41254.44 | 90749 | none |
| Kenai Peninsula Borough | Alaska | 49691 | 55400 | 58617 | 2.85 | 11.0 | 72.7 | 12.0 | 8.49 | no | some_college | 32050.39 | 65279 | none |
| Ketchikan Gateway Borough | Alaska | 14070 | 13477 | 13856 | 1.27 | 10.6 | 59.1 | 36.7 | 6.31 | no | some_college | 32635.69 | 67321 | none |
| Kodiak Island Borough | Alaska | 13913 | 13592 | 13448 | -4.48 | 9.3 | 59.2 | 25.9 | 5.10 | no | some_college | 29922.97 | 74167 | none |
| Lake and Peninsula Borough | Alaska | 1823 | 1631 | 1620 | -2.59 | 16.5 | 75.0 | 2.5 | 11.89 | no | hs_diploma | 20957.43 | 45208 | none |
| Matanuska-Susitna Borough | Alaska | 59322 | 88995 | 106532 | 11.14 | 9.8 | 79.2 | 10.1 | 8.66 | yes | some_college | 27306.48 | 74887 | none |
| Nome Census Area | Alaska | 9196 | 9492 | 9921 | 0.78 | 24.9 | 56.2 | 17.4 | 12.57 | no | hs_diploma | 21509.23 | 53821 | none |
| North Slope Borough | Alaska | 7385 | 9430 | 9782 | 0.06 | 10.2 | 48.3 | 24.9 | 7.44 | no | hs_diploma | 28886.59 | 77266 | none |
| Northwest Arctic Borough | Alaska | 7208 | 7523 | 7684 | -0.48 | 25.3 | 53.7 | 19.4 | 16.82 | no | hs_diploma | 19824.44 | 61533 | none |
| Petersburg Borough | Alaska | 6684 | 3815 | 3281 | -0.18 | 7.8 | 76.7 | 9.5 | 9.34 | no | some_college | 33142.29 | 63490 | NA |
| Prince of Wales-Hyder Census Area | Alaska | 6146 | 5559 | 6443 | -0.05 | 16.0 | 69.0 | 9.7 | 11.42 | no | some_college | 23990.18 | 52114 | NA |
| Sitka City and Borough | Alaska | 8835 | 8881 | 8689 | -3.05 | 9.2 | 55.9 | 24.4 | 4.68 | no | some_college | 35002.92 | 70765 | none |
| Skagway | Alaska | NA | 968 | NA | NA | 5.6 | 59.1 | 27.2 | 10.56 | no | some_college | 38150.23 | 70673 | NA |
| Southeast Fairbanks Census Area | Alaska | 6174 | 7029 | 6888 | -1.32 | 13.9 | 65.2 | 17.3 | 10.44 | no | some_college | 24596.05 | 63866 | none |
| Valdez-Cordova Census Area | Alaska | 10195 | 9636 | 9278 | -5.06 | 7.4 | 71.8 | 17.6 | 7.96 | no | some_college | 30746.27 | 86019 | none |
| Kusilvak Census Area | Alaska | 7028 | 7459 | 8202 | 2.91 | NA | 64.8 | 4.1 | NA | NA | NA | NA | NA | none |
| Wrangell | Alaska | NA | 2369 | NA | NA | 11.7 | 78.7 | 11.9 | 7.71 | no | some_college | 30153.57 | 56094 | NA |
| Yakutat City and Borough | Alaska | 808 | 662 | 605 | -7.07 | 6.2 | 61.1 | 12.4 | 9.36 | no | some_college | 29311.67 | 64583 | NA |
| Yukon-Koyukuk Census Area | Alaska | 6551 | 5588 | 5365 | -3.52 | 25.5 | 69.1 | 2.9 | 18.26 | no | hs_diploma | 19447.74 | 37819 | none |
| Apache County | Arizona | 69423 | 71518 | 71606 | -0.95 | 35.9 | 76.3 | 5.2 | 10.42 | no | hs_diploma | 12119.78 | 32360 | NA |
| Cochise County | Arizona | 117755 | 131346 | 124756 | -3.54 | 18.1 | 69.0 | 12.2 | 5.61 | yes | some_college | 26016.10 | 47847 | NA |
| Coconino County | Arizona | 116320 | 134421 | 140776 | 3.17 | 21.0 | 61.2 | 18.9 | 5.55 | yes | some_college | 27266.04 | 53523 | none |
| Gila County | Arizona | 51335 | 53597 | 53501 | 0.98 | 21.9 | 78.3 | 4.8 | 6.06 | no | some_college | 22383.06 | 41179 | NA |
| variable | description | |
|---|---|---|
| 1 | name | Name of county. |
| 2 | state | Name of state. |
| 3 | pop2000 | Population in 2000. |
| 4 | pop2010 | Population in 2010. |
| 5 | pop2017 | Population in 2017. |
| 6 | pop_change | Population change from 2010 to 2017 (in percent). |
| 7 | poverty | Percent of population in poverty in 2017. |
| 8 | homeownership | Homeownership rate, 2006-2010. |
| 9 | multi_unit | Multi-unit rate: percent of housing units that are in multi-unit structures, 2006-2010. |
| 10 | unemployment_rate | Unemployment rate in 2017. |
| 11 | metro | Whether the county contains a metropolitan area, taking one of the values yes or no. |
| 12 | median_edu | Median education level (2013-2017), taking one of the values below_hs, hs_diploma, some_college, or bachelors. |
| 13 | per_capita_income | Per capita (per person) income (2013-2017). |
| 14 | median_hh_income | Median household income. |
| 15 | smoking_ban | Describes the type of county-level smoking ban in place in 2010, taking one of the values none, partial, or comprehensive. |
Data were collected about students in a statistics course. Three variables were recorded for each student: number of siblings, student height, and whether the student had previously taken a statistics course. Classify each of the variables as continuous numerical, discrete numerical, or categorical.
An experiment is evaluating the effectiveness of a new drug in
treating migraines. A group variable is used to indicate
the experiment group for each patient: treatment or control. The
num_migraines variable represents the number of migraines
the patient experienced during a 3-month period. Classify each variable
as either numerical or categorical?
homeownership: the percentage of homes that are owned
by residentsmulti-unit: the percentage of housing units that are in
multi-unit structures (e.g., apartments, condos)Are these two variables related?
| name | state | homeownership | multi_unit |
|---|---|---|---|
| Autauga County | Alabama | 77.5 | 7.2 |
| Baldwin County | Alabama | 76.7 | 22.6 |
| Barbour County | Alabama | 68.0 | 11.1 |
| Bibb County | Alabama | 82.9 | 6.6 |
| Blount County | Alabama | 82.0 | 3.7 |
| Bullock County | Alabama | 76.9 | 9.9 |
| Butler County | Alabama | 69.0 | 13.7 |
| Calhoun County | Alabama | 70.7 | 14.3 |
| Chambers County | Alabama | 71.4 | 8.7 |
| Cherokee County | Alabama | 77.5 | 4.3 |
| Chilton County | Alabama | 75.1 | 4.4 |
| Choctaw County | Alabama | 85.6 | 3.9 |
| Clarke County | Alabama | 80.0 | 6.3 |
| Clay County | Alabama | 72.8 | 11.2 |
| Cleburne County | Alabama | 74.9 | 5.3 |
| Coffee County | Alabama | 69.7 | 13.6 |
| Colbert County | Alabama | 73.5 | 12.3 |
| Conecuh County | Alabama | 81.6 | 6.0 |
| Coosa County | Alabama | 83.7 | 1.9 |
| Covington County | Alabama | 74.0 | 6.1 |
| Crenshaw County | Alabama | 67.8 | 9.2 |
| Cullman County | Alabama | 74.7 | 8.5 |
| Dale County | Alabama | 61.2 | 13.2 |
| Dallas County | Alabama | 62.6 | 16.0 |
| DeKalb County | Alabama | 77.5 | 6.4 |
| Elmore County | Alabama | 77.6 | 7.0 |
| Escambia County | Alabama | 73.5 | 7.8 |
| Etowah County | Alabama | 73.0 | 11.9 |
| Fayette County | Alabama | 76.0 | 7.9 |
| Franklin County | Alabama | 69.2 | 10.4 |
| Geneva County | Alabama | 71.6 | 6.6 |
| Greene County | Alabama | 71.1 | 11.1 |
| Hale County | Alabama | 74.3 | 6.1 |
| Henry County | Alabama | 81.9 | 3.2 |
| Houston County | Alabama | 67.4 | 15.2 |
| Jackson County | Alabama | 76.6 | 5.8 |
| Jefferson County | Alabama | 66.8 | 24.0 |
| Lamar County | Alabama | 75.1 | 9.0 |
| Lauderdale County | Alabama | 73.0 | 14.7 |
| Lawrence County | Alabama | 78.7 | 5.1 |
| Lee County | Alabama | 64.2 | 23.3 |
| Limestone County | Alabama | 77.1 | 9.4 |
| Lowndes County | Alabama | 75.4 | 7.0 |
| Macon County | Alabama | 68.0 | 15.5 |
| Madison County | Alabama | 70.4 | 21.4 |
| Marengo County | Alabama | 73.5 | 8.3 |
| Marion County | Alabama | 75.8 | 10.9 |
| Marshall County | Alabama | 72.5 | 9.3 |
| Mobile County | Alabama | 68.4 | 17.7 |
| Monroe County | Alabama | 73.8 | 6.0 |
| Montgomery County | Alabama | 63.2 | 22.4 |
| Morgan County | Alabama | 73.1 | 13.7 |
| Perry County | Alabama | 67.8 | 11.4 |
| Pickens County | Alabama | 74.1 | 10.1 |
| Pike County | Alabama | 56.3 | 18.7 |
| Randolph County | Alabama | 75.9 | 4.8 |
| Russell County | Alabama | 62.3 | 17.8 |
| St. Clair County | Alabama | 82.2 | 5.5 |
| Shelby County | Alabama | 80.6 | 11.4 |
| Sumter County | Alabama | 68.3 | 14.5 |
| Talladega County | Alabama | 73.0 | 9.6 |
| Tallapoosa County | Alabama | 73.3 | 8.9 |
| Tuscaloosa County | Alabama | 63.3 | 25.4 |
| Walker County | Alabama | 77.7 | 6.6 |
| Washington County | Alabama | 83.0 | 2.6 |
| Wilcox County | Alabama | 76.8 | 6.0 |
| Winston County | Alabama | 73.8 | 6.1 |
| Aleutians East Borough | Alaska | 59.2 | 11.8 |
| Aleutians West Census Area | Alaska | 36.3 | 30.9 |
| Anchorage Municipality | Alaska | 61.7 | 35.3 |
| Bethel Census Area | Alaska | 61.3 | 13.9 |
| Bristol Bay Borough | Alaska | 56.6 | 13.4 |
| Denali Borough | Alaska | 60.7 | 14.1 |
| Dillingham Census Area | Alaska | 60.7 | 14.1 |
| Fairbanks North Star Borough | Alaska | 59.8 | 26.2 |
| Haines Borough | Alaska | 74.5 | 13.2 |
| Hoonah Angoon Census Area | Alaska | 64.0 | 8.6 |
| Juneau City and Borough | Alaska | 64.0 | 32.2 |
| Kenai Peninsula Borough | Alaska | 72.7 | 12.0 |
| Ketchikan Gateway Borough | Alaska | 59.1 | 36.7 |
| Kodiak Island Borough | Alaska | 59.2 | 25.9 |
| Lake and Peninsula Borough | Alaska | 75.0 | 2.5 |
| Matanuska-Susitna Borough | Alaska | 79.2 | 10.1 |
| Nome Census Area | Alaska | 56.2 | 17.4 |
| North Slope Borough | Alaska | 48.3 | 24.9 |
| Northwest Arctic Borough | Alaska | 53.7 | 19.4 |
| Petersburg Borough | Alaska | 76.7 | 9.5 |
| Prince of Wales-Hyder Census Area | Alaska | 69.0 | 9.7 |
| Sitka City and Borough | Alaska | 55.9 | 24.4 |
| Skagway | Alaska | 59.1 | 27.2 |
| Southeast Fairbanks Census Area | Alaska | 65.2 | 17.3 |
| Valdez-Cordova Census Area | Alaska | 71.8 | 17.6 |
| Kusilvak Census Area | Alaska | 64.8 | 4.1 |
| Wrangell | Alaska | 78.7 | 11.9 |
| Yakutat City and Borough | Alaska | 61.1 | 12.4 |
| Yukon-Koyukuk Census Area | Alaska | 69.1 | 2.9 |
| Apache County | Arizona | 76.3 | 5.2 |
| Cochise County | Arizona | 69.0 | 12.2 |
| Coconino County | Arizona | 61.2 | 18.9 |
| Gila County | Arizona | 78.3 | 4.8 |
| Graham County | Arizona | 72.0 | 7.7 |
| Greenlee County | Arizona | 46.9 | 6.1 |
| La Paz County | Arizona | 75.4 | 3.6 |
| Maricopa County | Arizona | 66.3 | 25.1 |
| Mohave County | Arizona | 71.5 | 9.8 |
| Navajo County | Arizona | 72.5 | 7.0 |
| Pima County | Arizona | 64.6 | 22.9 |
| Pinal County | Arizona | 77.7 | 6.3 |
| Santa Cruz County | Arizona | 71.0 | 17.6 |
| Yavapai County | Arizona | 72.5 | 11.0 |
| Yuma County | Arizona | 69.6 | 12.5 |
| Arkansas County | Arkansas | 64.4 | 10.9 |
| Ashley County | Arkansas | 72.4 | 8.5 |
| Baxter County | Arkansas | 76.6 | 10.1 |
| Benton County | Arkansas | 70.1 | 15.6 |
| Boone County | Arkansas | 72.7 | 12.1 |
| Bradley County | Arkansas | 70.2 | 8.0 |
| Calhoun County | Arkansas | 82.1 | 2.4 |
| Carroll County | Arkansas | 69.5 | 11.6 |
| Chicot County | Arkansas | 69.6 | 10.0 |
| Clark County | Arkansas | 67.6 | 15.9 |
| Clay County | Arkansas | 74.0 | 8.1 |
| Cleburne County | Arkansas | 77.9 | 5.7 |
| Cleveland County | Arkansas | 78.0 | 3.1 |
| Columbia County | Arkansas | 69.8 | 11.4 |
| Conway County | Arkansas | 75.8 | 6.3 |
| Craighead County | Arkansas | 61.2 | 20.0 |
| Crawford County | Arkansas | 73.0 | 10.8 |
| Crittenden County | Arkansas | 58.2 | 23.1 |
| Cross County | Arkansas | 70.7 | 11.3 |
| Dallas County | Arkansas | 70.5 | 7.9 |
| Desha County | Arkansas | 59.1 | 17.2 |
| Drew County | Arkansas | 67.5 | 7.7 |
| Faulkner County | Arkansas | 66.4 | 17.3 |
| Franklin County | Arkansas | 78.8 | 4.7 |
| Fulton County | Arkansas | 79.6 | 3.4 |
| Garland County | Arkansas | 70.1 | 16.7 |
| Grant County | Arkansas | 80.3 | 2.4 |
| Greene County | Arkansas | 65.7 | 13.5 |
| Hempstead County | Arkansas | 68.4 | 10.2 |
| Hot Spring County | Arkansas | 76.0 | 4.4 |
| Howard County | Arkansas | 69.6 | 8.2 |
| Independence County | Arkansas | 72.8 | 7.3 |
| Izard County | Arkansas | 79.7 | 4.5 |
| Jackson County | Arkansas | 69.8 | 15.0 |
| Jefferson County | Arkansas | 64.4 | 14.8 |
| Johnson County | Arkansas | 68.8 | 11.3 |
| Lafayette County | Arkansas | 79.2 | 5.4 |
| Lawrence County | Arkansas | 67.2 | 8.1 |
| Lee County | Arkansas | 66.3 | 13.9 |
| Lincoln County | Arkansas | 69.3 | 8.4 |
| Little River County | Arkansas | 71.2 | 9.4 |
| Logan County | Arkansas | 79.1 | 4.0 |
| Lonoke County | Arkansas | 74.4 | 8.6 |
| Madison County | Arkansas | 75.3 | 3.6 |
| Marion County | Arkansas | 81.6 | 4.7 |
| Miller County | Arkansas | 66.3 | 18.7 |
| Mississippi County | Arkansas | 59.9 | 16.8 |
| Monroe County | Arkansas | 61.4 | 16.1 |
| Montgomery County | Arkansas | 82.8 | 2.5 |
| Nevada County | Arkansas | 71.3 | 5.9 |
| Newton County | Arkansas | 79.7 | 4.0 |
| Ouachita County | Arkansas | 69.8 | 10.5 |
| Perry County | Arkansas | 81.7 | 2.3 |
| Phillips County | Arkansas | 54.7 | 15.7 |
| Pike County | Arkansas | 74.8 | 6.1 |
| Poinsett County | Arkansas | 66.4 | 11.5 |
| Polk County | Arkansas | 77.4 | 3.7 |
| Pope County | Arkansas | 69.7 | 14.1 |
| Prairie County | Arkansas | 72.6 | 5.8 |
| Pulaski County | Arkansas | 60.4 | 24.9 |
| Randolph County | Arkansas | 76.6 | 6.8 |
| St. Francis County | Arkansas | 58.7 | 15.2 |
| Saline County | Arkansas | 77.7 | 7.8 |
| Scott County | Arkansas | 75.1 | 6.4 |
| Searcy County | Arkansas | 75.0 | 4.7 |
| Sebastian County | Arkansas | 63.4 | 22.3 |
| Sevier County | Arkansas | 74.2 | 6.1 |
| Sharp County | Arkansas | 80.8 | 3.6 |
| Stone County | Arkansas | 80.4 | 1.4 |
| Union County | Arkansas | 71.2 | 8.8 |
| Van Buren County | Arkansas | 78.5 | 9.9 |
| Washington County | Arkansas | 56.3 | 30.1 |
| White County | Arkansas | 69.0 | 13.8 |
| Woodruff County | Arkansas | 61.5 | 12.9 |
| Yell County | Arkansas | 70.1 | 7.3 |
| Alameda County | California | 55.1 | 38.0 |
| Alpine County | California | 73.4 | 38.4 |
| Amador County | California | 77.3 | 7.5 |
| Butte County | California | 61.2 | 19.7 |
| Calaveras County | California | 78.8 | 3.7 |
| Colusa County | California | 64.4 | 14.3 |
| Contra Costa County | California | 69.5 | 23.8 |
| Del Norte County | California | 60.9 | 14.6 |
| El Dorado County | California | 76.5 | 12.1 |
| Fresno County | California | 55.0 | 25.8 |
| Glenn County | California | 67.5 | 11.4 |
| Humboldt County | California | 57.6 | 18.9 |
| Imperial County | California | 56.6 | 21.4 |
| Inyo County | California | 64.0 | 13.1 |
| Kern County | California | 61.4 | 18.1 |
| Kings County | California | 56.0 | 18.5 |
| Lake County | California | 67.1 | 7.8 |
| Lassen County | California | 63.7 | 9.7 |
| Los Angeles County | California | 48.2 | 41.8 |
| Madera County | California | 63.0 | 12.0 |
| Marin County | California | 64.0 | 27.0 |
| Mariposa County | California | 70.0 | 8.0 |
| Mendocino County | California | 62.8 | 13.1 |
| Merced County | California | 55.9 | 17.3 |
| Modoc County | California | 70.2 | 5.3 |
| Mono County | California | 56.4 | 51.1 |
| Monterey County | California | 53.4 | 26.6 |
| Napa County | California | 65.1 | 19.7 |
| Nevada County | California | 74.0 | 9.5 |
| Orange County | California | 60.8 | 33.7 |
| Placer County | California | 72.9 | 17.1 |
| Plumas County | California | 65.6 | 6.6 |
| Riverside County | California | 70.0 | 16.1 |
| Sacramento County | California | 59.5 | 26.9 |
| San Benito County | California | 64.3 | 14.3 |
| San Bernardino County | California | 65.1 | 18.8 |
| San Diego County | California | 55.9 | 35.5 |
| San Francisco County | California | 37.5 | 66.6 |
| San Joaquin County | California | 61.7 | 18.7 |
| San Luis Obispo County | California | 61.4 | 17.7 |
| San Mateo County | California | 61.1 | 32.4 |
| Santa Barbara County | California | 54.1 | 29.5 |
| Santa Clara County | California | 59.2 | 32.8 |
| Santa Cruz County | California | 59.6 | 21.4 |
| Shasta County | California | 66.0 | 16.0 |
| Sierra County | California | 80.1 | 4.5 |
| Siskiyou County | California | 65.2 | 14.4 |
| Solano County | California | 65.8 | 21.4 |
| Sonoma County | California | 62.4 | 18.8 |
| Stanislaus County | California | 62.1 | 16.5 |
| Sutter County | California | 61.8 | 20.0 |
| Tehama County | California | 65.1 | 11.6 |
| Trinity County | California | 73.5 | 7.1 |
| Tulare County | California | 59.3 | 14.4 |
| Tuolumne County | California | 70.2 | 8.6 |
| Ventura County | California | 66.4 | 20.2 |
| Yolo County | California | 54.1 | 30.6 |
| Yuba County | California | 59.8 | 17.8 |
| Adams County | Colorado | 68.4 | 23.9 |
| Alamosa County | Colorado | 63.2 | 20.3 |
| Arapahoe County | Colorado | 65.9 | 33.7 |
| Archuleta County | Colorado | 82.9 | 17.0 |
| Baca County | Colorado | 74.9 | 4.4 |
| Bent County | Colorado | 67.4 | 8.9 |
| Boulder County | Colorado | 63.9 | 28.2 |
| Broomfield County | Colorado | 74.4 | 21.7 |
| Chaffee County | Colorado | 76.9 | 7.4 |
| Cheyenne County | Colorado | 80.5 | 5.6 |
| Clear Creek County | Colorado | 81.3 | 11.8 |
| Conejos County | Colorado | 75.7 | 4.1 |
| Costilla County | Colorado | 74.6 | 7.3 |
| Crowley County | Colorado | 74.0 | 6.5 |
| Custer County | Colorado | 80.5 | 4.7 |
| Delta County | Colorado | 74.3 | 5.3 |
| Denver County | Colorado | 52.5 | 44.9 |
| Dolores County | Colorado | 78.3 | 1.7 |
| Douglas County | Colorado | 82.5 | 14.9 |
| Eagle County | Colorado | 65.3 | 36.3 |
| Elbert County | Colorado | 91.3 | 1.4 |
| El Paso County | Colorado | 66.6 | 22.4 |
| Fremont County | Colorado | 76.6 | 10.0 |
| Garfield County | Colorado | 67.5 | 20.5 |
| Gilpin County | Colorado | 71.8 | 11.3 |
| Grand County | Colorado | 76.9 | 30.3 |
| Gunnison County | Colorado | 59.1 | 28.8 |
| Hinsdale County | Colorado | 83.5 | 3.6 |
| Huerfano County | Colorado | 72.1 | 8.6 |
| Jackson County | Colorado | 72.3 | 5.6 |
| Jefferson County | Colorado | 71.9 | 24.7 |
| Kiowa County | Colorado | 66.6 | 3.4 |
| Kit Carson County | Colorado | 69.3 | 10.7 |
| Lake County | Colorado | 66.9 | 17.7 |
| La Plata County | Colorado | 69.1 | 18.7 |
| Larimer County | Colorado | 67.5 | 21.4 |
| Las Animas County | Colorado | 69.5 | 12.0 |
| Lincoln County | Colorado | 70.8 | 11.8 |
| Logan County | Colorado | 68.3 | 15.0 |
| Mesa County | Colorado | 72.3 | 14.8 |
| Mineral County | Colorado | 86.4 | 0.2 |
| Moffat County | Colorado | 75.1 | 14.0 |
| Montezuma County | Colorado | 72.8 | 9.5 |
| Montrose County | Colorado | 74.6 | 8.9 |
| Morgan County | Colorado | 67.3 | 12.1 |
| Otero County | Colorado | 66.1 | 13.3 |
| Ouray County | Colorado | 74.3 | 8.1 |
| Park County | Colorado | 87.9 | 1.3 |
| Phillips County | Colorado | 73.3 | 7.6 |
| Pitkin County | Colorado | 62.5 | 40.0 |
| Prowers County | Colorado | 66.7 | 14.9 |
| Pueblo County | Colorado | 69.9 | 16.2 |
| Rio Blanco County | Colorado | 74.1 | 13.8 |
| Rio Grande County | Colorado | 78.9 | 8.9 |
| Routt County | Colorado | 74.1 | 28.8 |
| Saguache County | Colorado | 68.3 | 8.1 |
Suppose that \(X\) and \(Y\) are associated varaibles.
There are two primary types of data collection: experiments and observational studies.
county data set).Researchers collected data to examine the relationship between air pollutants and preterm births in Southern California. During the study air pollution levels were measured by air quality monitoring stations. Specifically, levels of carbon monoxide were recorded in parts per million, nitrogen dioxide and ozone in parts per hundred million, and coarse particulate matter (PM\(_{10}\)) in \(\mu g/m^3\). Length of gestation data were collected on 143,196 births between the years 1989 and 1993, and air pollution exposure during gestation was calculated for each birth. The analysis suggested that increased ambient PM\(_{10}\) and, to a lesser degree, CO concentrations may be associated with the occurrence of preterm births.
Researchers collected data to examine the relationship
between air pollutants and preterm births in Southern California. During
the study air pollution levels were measured by air quality monitoring
stations. Specifically, levels of carbon monoxide were recorded in parts
per million, nitrogen dioxide and ozone in parts per hundred million,
and coarse particulate matter (PM\(_{10}\)) in \(\mu
g/m^3\). Length of gestation data were collected on 143,196
births between the years 1989 and 1993, and air pollution exposure
during gestation was calculated for each birth. The analysis suggested
that increased ambient PM\(_{10}\) and,
to a lesser degree, CO concentrations may be associated with the
occurrence of preterm births.
A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlled study where 89 individuals who identified as female diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. Forty-three (43) patients in the treatment group received acupuncture that is specifically designed to treat migraines. Forty-six (46) patients in the control group received placebo acupuncture (needle insertion at non-acupoint locations). Twenty-four (24) hours after patients received acupuncture, they were asked if they were pain free. Results are summarized in the contingency table below. Also provided is a figure from the original paper displaying the appropriate area (M) versus the inappropriate area (S) used in the treatment of migraine attacks.
|
Pain free?
|
||
|---|---|---|
| Group | No | Yes |
| Control | 44 | 2 |
| Treatment | 33 | 10 |
What percent of patients in the treatment group were pain free 24 hours after receiving acupuncture?
What percent were pain free in the control group?
In which group did a higher percent of patients become pain free 24 hours after receiving acupuncture?
What are the explanatory and response variables in this study? Classify each as numerical or categorical.